| Title:
|
Stability of Tangential Locally Conformal Symplectic Forms (English) |
| Author:
|
Ida, Cristian |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
81-89 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we firstly define a tangential Lichnerowicz cohomology on foliated manifolds. Next, we define tangential locally conformal symplectic forms on a foliated manifold and we formulate and prove some results concerning their stability. (English) |
| Keyword:
|
foliated manifold |
| Keyword:
|
tangential Lichnerowicz cohomology |
| Keyword:
|
tangential locally conformal symplectic structure |
| Keyword:
|
stability |
| MSC:
|
53C12 |
| MSC:
|
53D99 |
| MSC:
|
57R17 |
| MSC:
|
58A12 |
| idZBL:
|
Zbl 1318.53018 |
| idMR:
|
MR3331072 |
| . |
| Date available:
|
2014-09-01T08:09:23Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143917 |
| . |
| Reference:
|
[1] Banyaga, A.: Some properties of locally conformal symplectic structures. Comment. Math. Helv. 77, 2 (2002), 383–398. Zbl 1020.53050, MR 1915047, 10.1007/s00014-002-8345-z |
| Reference:
|
[2] Banyaga, A.: Examples of non $d_{\omega }$-exact locally conformal symplectic forms. Journal of Geometry 87, 1-2 (2007), 1–13. Zbl 1157.53040, MR 2372512, 10.1007/s00022-006-1849-8 |
| Reference:
|
[3] Bande, G., Kotschick, D.: Moser stability for locally conformally symplectic structures. Proc. Amer. Math. Soc. 137 (2009), 2419–2424. Zbl 1176.53081, MR 2495277, 10.1090/S0002-9939-09-09821-9 |
| Reference:
|
[4] Bott, R., Tu, L. W.: Differential Forms in Algebraic Topology. Graduate Text in Math. 82 Springer-Verlag, Berlin, 1982. Zbl 0496.55001, MR 0658304 |
| Reference:
|
[5] Datta, M., Islam, Md R.: Smooth maps of a foliated manifold in a symplectic manifold. Proc. Indian Acad. Sci. (Math. Sci.) 119, 3 (2009), 333–343. Zbl 1173.53309, MR 2547696, 10.1007/s12044-009-0025-0 |
| Reference:
|
[6] Giachetta, G., Mangiarotti, L., Sardanashvily, G.: Geometric and Algebraic Toplogical Methods in Quantum Mechanics. World Scientific, Singapore, 2005. MR 2218620 |
| Reference:
|
[7] Guedira, F., Lichnerowicz, A.: Geometrie des algebres de Lie locales de Kirillov. J. Math. Pures et Appl. 63 (1984), 407–484. Zbl 0562.53029, MR 0789560 |
| Reference:
|
[8] Haller, S., Rybicki, T.: On the Group of Diffeomorphisms Preserving a Locally Conformal Symplectic Structure. Annals of Global Analysis and Geometry 17, 5 (1999), 475–502. Zbl 0940.53044, MR 1715157, 10.1023/A:1006650124434 |
| Reference:
|
[9] Hector, G., Macias, E., Saralegi, M.: Lemme de Moser feuilleté et classification des variétés de Poisson réguliéres. Publ. Mat. 33 (1989), 423–430. Zbl 0716.58011, MR 1038481, 10.5565/PUBLMAT_33389_04 |
| Reference:
|
[10] El Kacimi, A. A.: Sur la cohomologie feuilletée. Compositio Mathematica 49, 2 (1983), 195–215. Zbl 0516.57017, MR 0704391 |
| Reference:
|
[11] Lee, H. C.: A kind of even-dimensional differential geometry and its application to exterior calculus. Amer. J. Math. 65 (1943), 433–438. Zbl 0060.38302, MR 0008495, 10.2307/2371967 |
| Reference:
|
[12] de León, M., López, B., Marrero, J. C., Padrón, E.: On the computation of the Lichnerowicz–Jacobi cohomology. J. Geom. Phys. 44 (2003), 507–522. Zbl 1092.53060, MR 1943175, 10.1016/S0393-0440(02)00056-6 |
| Reference:
|
[13] Lichnerowicz, A.: Les variétés de Poisson et leurs algébres de Lie associées. J. Differential Geom. 12, 2 (1977), 253–300. Zbl 0405.53024, MR 0501133 |
| Reference:
|
[14] Molino, P.: Riemannian foliations. Progress in Mathematics 73 Birkhäuser, Boston, 1988. Zbl 0668.57023, MR 0932463 |
| Reference:
|
[15] Moore, C. C., Schochet, C.: Global Analysis on Foliated Spaces. MSRI Publications 9 Springer-Verlag, New York, 1988. Zbl 0648.58034, MR 0918974 |
| Reference:
|
[16] Moser, J.: On the volume elements on a manifold. Trans. Amer. Math. Soc. 120 (1965), 286–294. Zbl 0141.19407, MR 0182927, 10.1090/S0002-9947-1965-0182927-5 |
| Reference:
|
[17] Mümken, B.: On Tangential Cohomology of Riemannian Foliations. American J. Math. 128, 6 (2006), 1391–1408. Zbl 1111.53025, MR 2275025, 10.1353/ajm.2006.0047 |
| Reference:
|
[18] Novikov, S. P.: The Hamiltonian formalism and a multivalued analogue of Morse theory. Uspekhi Mat. Nauk 37 (1982), 3-49. (1982), 3–49 (in Russian). MR 0676612 |
| Reference:
|
[19] Ornea, L., Verbitsky, M.: Morse–Novikov cohomology of locally conformally Kähler manifolds. J. of Geometry and Physics 59 (2009), 295–305. Zbl 1161.57015, MR 2501742, 10.1016/j.geomphys.2008.11.003 |
| Reference:
|
[20] Rybicki, T.: On foliated, Poisson and Hamiltonian diffeomorphisms. Diff. Geom. Appl. 15 (2001), 33–46. Zbl 0988.22010, MR 1845174, 10.1016/S0926-2245(01)00042-0 |
| Reference:
|
[21] Tondeur, Ph.: Foliations on Riemannian Manifolds. Universitext, Springer-Verlag, 1988. Zbl 0643.53024, MR 0934020 |
| Reference:
|
[22] Vaisman, I.: Variétés riemanniene feuilletées. Czechoslovak Math. J. 21 (1971), 46–75. |
| Reference:
|
[23] Vaisman, I.: Remarkable operators and commutation formulas on locally conformal Kähler manifolds. Compositio Math. 40, 3 (1980), 287–299. Zbl 0401.53019, MR 0571051 |
| Reference:
|
[24] Vaisman, I.: Locally conformal symplectic manifolds. Internat. J. Math. and Math. Sci. 8, 3 (1985), 521–536. Zbl 0585.53030, MR 0809073 |
| . |
